Factor ax^2-ay^2+bx^2-by^2

$a x^{2} - a y^{2} + b x^{2} - b y^{2}$

Step 1

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(a x^{2} - a y^{2}) + b x^{2} - b y^{2}$

Factor out the greatest common factor (GCF) from each group.

$a (x^{2} - 1 y^{2}) + b (x^{2} - 1 y^{2})$

Step 2

Factor the polynomial by factoring out the greatest common factor, $x^{2} - 1 y^{2}$ .

$(x^{2} - 1 y^{2}) (a + b)$

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = y$ .

$(x + y) (x - y) (a + b)$